In this paper, we present the design of a high resolution Chirp Transform Spectrometer (CTS) which is part of the GREAT (German REceiver for Astronomy at Terahertz frequencies) instrument onboard SOFIA, the Stratospheric Observatory For Infrared Astronomy. The new spectrometer will provide unique spectral resolving power and linearity response, since the analog Fourier transform performed by the CTS spectrometer was improved through a new design, that we call "Adaptive Digital Chirp Processor (ADCP)". The principle behind the ADCP consists on digitally generating the dispersive signal which adapts to the compressor dispersive properties, achieving maximum spectral resolution and higher dynamic range. Excellent test results have been obtained such as a white noise dynamic range of 30 dB, and a spectral resolution (FWHM) of 41.68 kHz which would mean if analyzing signals with the high frequency band receiver on the GREAT instrument (4.7 THz) a spectral resolving power (λ/ λ) higher than 10 8 .